Thank you very much for the additional information on Morgan. She sounds like a very sweet girl.
Typically, although rare, we see dogs vomit up hairballs if they have them... The coughing indicates irritation of the throat, trachea, or lower airways...I suppose there could be a hair irritating her airways, but mineral oil won't help there.
You could use a feline Hairball product available at many pet stores, if you would like to try something similar.
However, I do want you to know that I'm concerned that there is something else going on. At this point, because of her age, and because she is a Pom, I would recommend having her evaluated by your veterinarian as soon as possible.
Morgan may have a condition called Collapsing Trachea. This will require x-rays to diagnose. It would be unusual for this condition to develop in a dog her age without a history of an occasional cough, but I have seen this happen. The cough is a dry, honking cough.
Another common cause of cough in older, small breed dogs: if she has dental
disease or infection in her mouth, it is common for these dogs to inhale bacteria from within her mouth that becomes aerosolized from breathing. This bacteria can infect her throat, trachea, and other airways, and can cause coughing. Antibiotics may be needed.
Also, and I don't want to concern you, but any sudden onset of coughing in a senior dog
could indicate heart disease. Coughing can be the only sign in some pets. Your vet can carefully listen to her lungs and heart for evidence of fluid or a murmur, and may recommend chest x-rays (that could also include the trachea) to help rule out infection, heart enlargement, collapsing trachea, and masses.
Definitely don't give her any cough suppressants. I don't recommend the mineral oil at this time.
I hope this information helps - please let me know how else I can assist both you and Morgan.